Question

when a man observed a sobriety checkpoint conducted by a police department, he saw 652 drivers were screened and 4 were arrested for driving while intoxicated. based on those results, we can estimate that p(w)=0.00613, where w denotes the event of screening a driver and getting someone who is intoxicated. what does p(\\(\overline{w}\\)) denote, and what is its value? what does p(\\(\overline{w}\\)) represent? a. p(\\(\overline{w}\\)) denotes the probability of screening a driver and finding that he or she is not intoxicated. b. p(\\(\overline{w}\\)) denotes the probability of a driver passing through the sobriety checkpoint. c. p(\\(\overline{w}\\)) denotes the probability of driver being intoxicated. d. p(\\(\overline{w}\\)) denotes the probability of screening a driver and finding that he or she is intoxicated. p(\\(\overline{w}\\)) = (round to five decimal places as needed.)

Explanation:

Step1: Recall probability - complement rule

The event $\overline{W}$ is the complement of event $W$. For any event $A$, $P(A)+P(\overline{A}) = 1$. Here, $W$ is the event of screening a driver and getting someone who is intoxicated, so $\overline{W}$ is the event of screening a driver and getting someone who is not intoxicated.

Step2: Calculate $P(\overline{W})$

Given $P(W)=0.00613$, using the formula $P(\overline{W})=1 - P(W)$. So $P(\overline{W})=1 - 0.00613=0.99387$.

Answer:

A. $P(\overline{W})$ denotes the probability of screening a driver and finding that he or she is not intoxicated.
$P(\overline{W}) = 0.99387$